Beginning Algebra

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This clear, accessible treatment of mathematics features a building-block approach toward problem solving, realistic and diverse applications, and chapter organizer to help users focus their study and become effective and confident problem solvers. The Putting Your Skills to Work and new chapter-end feature, Math in the Media, present readers with opportunities to utilize critical thinking skills, analyze and interpret data, and problem solve using applied situations encountered in daily life. Earlier coverage of the Order of Arithmetic Operations--now section 1.5 so that operations is now covered together before Introduction to Algebra. The discussion of solving linear equations in Chapter 2 now includes coverage of equations with no solution and equations with infinitely many solutions. Section 4.3 now offers a more thorough introduction to polynomials, with the addition of new terminology at the beginning of the section and a new lesson on evaluating polynomials at the end. Revised Ch. 7 on Graphing and Functions includes new coverage of the rectangular coordinate system and slope. The coverage of the rectangular coordinate system in Chapter 7 has been improved for greater clarity.

To the Student

i

Preface

xiii

Acknowledgments

xx

Diagnostic Pretest

xxiv

A Brief Review of Arithmetic Skills

1

(66)

Simplifying Fractions

2

(8)

Adding and Subtracting Fractions

10

(10)

Multiplying and Dividing Fractions

20

(8)

Using Decimals

28

(12)

How Am I Doing? Sections 0.1--0.4

39

(1)

Using Percent

40

(7)

Rounding and Estimating

47

(5)

Using the Mathematics Blueprint for Problem Solving

52

(15)

Chapter 0 Organizer

60

(2)

Chapter 0 Review Problems

62

(3)

How Am I Doing? Chapter 0 Test

65

(2)

Real Numbers and Variables

67

(66)

Adding Real Numbers

68

(11)

Subtracting Real Numbers

79

(5)

Multiplying and Dividing Real Numbers

84

(10)

Exponents

94

(4)

The Order of Operations

98

(5)

How Am I Doing? Sections 1.1--1.5

102

(1)

Using the Distributive Property to Simplify Algebraic Expressions

103

(5)

Combining Like Terms

108

(5)

Using Substitution to Evaluate Algebraic Expressions and Formulas

113

(8)

Grouping Symbols

121

(12)

Chapter 1 Organizer

126

(1)

Chapter 1 Review Problems

127

(4)

How Am I Doing? Chapter 1 Test

131

(2)

Equations and Inequalities

133

(58)

The Addition Principle of Equality

134

(6)

The Multiplication Principle of Equality

140

(6)

Using the Addition and Multiplication Principles Together

146

(7)

Solving Equations with Fractions

153

(9)

How Am I Doing? Sections 2.1--2.4

161

(1)

Formulas

162

(8)

Writing and Graphing Inequalities

170

(5)

Solving Inequalities

175

(16)

Chapter 2 Organizer

184

(1)

Chapter 2 Review Problems

185

(4)

How Am I Doing? Chapter 2 Test

189

(1)

Cumulative Test for Chapters 0--2

190

(1)

Solving Applied Problems

191

(60)

Translating English Phrases into Algebraic Expressions

192

(6)

Using Equations to Solve Word Problems

198

(9)

Solving Word Problems: Comparisons

207

(7)

How Am I Doing? Sections 3.1--3.3

213

(1)

Solving Word Problems: The Value of Money and Percents

214

(10)

Solving Word Problems Using Geometric Formulas

224

(11)

Using Inequalities to Solve Word Problems

235

(16)

Chapter 3 Organizer

242

(1)

Chapter 3 Review Problems

243

(5)

How Am I Doing? Chapter 3 Test

248

(2)

Cumulative Test for Chapters 0--3

250

(1)

Exponents and Polynomials

251

(52)

The Rules of Exponents

252

(9)

Negative Exponents and Scientific Notation

261

(7)

Fundamental Polynomial Operations

268

(7)

How Am I Doing? Sections 4.1--4.3

274

(1)

Multiplying Polynomials

275

(6)

Multiplication: Special Cases

281

(7)

Dividing Polynomials

288

(15)

Chapter 4 Organizer

296

(1)

Chapter 4 Review Problems

297

(4)

How Am I Doing? Chapter 4 Test

301

(1)

Cumulative Test for Chapters 0--4

302

(1)

Factoring

303

(52)

Removing a Common Factor

304

(5)

Factoring by Grouping

309

(5)

Factoring Trinomials of the Form x2 + bx + c

314

(7)

Factoring Trinomials of the Form ax2 + bx + c

321

(7)

How Am I Doing? Sections 5.1--5.4

327

(1)

Special Cases of Factoring

328

(6)

A Brief Review of Factoring

334

(4)

Solving Quadratic Equations by Factoring

338

(17)

Chapter 5 Organizer

348

(1)

Chapter 5 Review Problems

349

(4)

How Am I Doing? Chapter 5 Test

353

(1)

Cumulative Test for Chapters 0--5

354

(1)

Rational Expressions and Equations

355

(50)

Simplifying Rational Expressions

356

(6)

Multiplying and Dividing Rational Expressions

362

(5)

Adding and Subtracting Rational Expressions

367

(9)

How Am I Doing? Sections 6.1--6.3

375

(1)

Simplifying Complex Rational Expressions

376

(5)

Solving Equations Involving Rational Expressions

381

(5)

Ratio, Proportion, and Other Applied Problems

386

(19)

Chapter 6 Organizer

396

(2)

Chapter 6 Review Problems

398

(5)

How Am I Doing? Chapter 6 Test

403

(1)

Cumulative Test for Chapters 0--6

404

(1)

Graphing and Functions

405

(66)

The Rectangular Coordinate System

406

(10)

Graphing Linear Equations

416

(10)

The Slope of a Line

426

(13)

How Am I Doing? Sections 7.1--7.3

437

(2)

Writing the Equation of a Line

439

(4)

Graphing Linear Inequalities

443

(5)

Functions

448

(23)

Chapter 7 Organizer

460

(2)

Chapter 7 Review Problems

462

(5)

How Am I Doing? Chapter 7 Test

467

(2)

Cumulative Test for Chapters 0--7

469

(2)

Systems of Equations

471

(46)

Solving a System of Equations in Two Variables by Graphing

472

(8)

Solving a System of Equations in Two Variables by the Substitution Method

480

(6)

Solving a System of Equations in Two Variables by the Addition Method

486

(9)

How Am I Doing? Sections 8.1--8.3

494

(1)

Review of Methods for Solving Systems of Equations

495

(5)

Solving Word Problems Using Systems of Equations

500

(17)

Chapter 8 Organizer

509

(2)

Chapter 8 Review Problems

511

(4)

How Am I Doing? Chapter 8 Test

515

(1)

Cumulative Test for Chapters 0--8

516

(1)

Radicals

517

(52)

Square Roots

518

(5)

Simplifying Radical Expressions

523

(5)

Adding and Subtracting Radical Expressions

528

(4)

Multiplying Radical Expressions

532

(6)

How Am I Doing? Sections 9.1--9.4

537

(1)

Dividing Radical Expressions

538

(6)

The Pythagorean Theorem and Radical Equations

544

(8)

Word Problems Involving Radicals: Direct and Inverse Variation

552

(17)

Chapter 9 Organizer

562

(1)

Chapter 9 Review Problems

563

(4)

How Am I Doing? Chapter 9 Test

567

(1)

Cumulative Test for Chapters 0--9

568

(1)

Quadratic Equations

569

(48)

Introduction to Quadratic Equations

570

(8)

Using the Square Root Property and Completing the Square to Find Solutions